Abhinav Kumar, Stony Brook University

Title: Twenty-four dimensional cannonballs and magic functions

Abstract: How can we pack oranges in a crate most efficiently? This classical question, or its idealized version - how to optimally pack n-dimensional space with congruent nonoverlapping spheres - has occupied the minds of scientists and mathematicians over many centuries.

Until recently, answers were provably known only up to dimension 3, the last being a massive feat of computer-assisted proof by Hales and his collaborators. In 2016 a breakthrough was achieved by Maryna Viazovska, who proved that the E8 root lattice gives the densest sphere packing in 8 dimensions. Shortly after, Cohn-Kumar-Miller-Radchenko-Viazovsa established that the Leech lattice gives rise to the densest sphere packing in 24 dimensions.

I will give a general introduction to the problem, the remarkable solution and some ideas of the proof, keeping assumed background to a minimum (the talk should be accessible to advanced undergraduates).